Where do I keep IOTA?

Completely new to cryptocurrency?

If so, it might be smart to keep your IOTA on an exchange until you learn more. The risks of keeping your balance on an exchange are well-documented, but the IOTA user experience is poor. This is now changing with the Trinity wallet, however.

Comfortable with technology, and have previous experience with cryptocurrency?

Given that you have the appropriate technical knowledge, it's safest to keep your balance in a personal wallet rather than on an exchange. Download the wallet & send a transaction from the exchange to your wallet.